A multiscale stochastic particle method based on the Fokker-Planck model for diatomic gas flows

Hypersonic flows in re-entry missions exhibit multiscale processes and strong non-equilibrium effects, posing significant challenges for numerical simulation. Traditional stochastic particle methods for non-equilibrium gas flows, such as the direct simulation Monte Carlo (DSMC), suffer from order degradation in near-continuum regimes, resulting in reduced accuracy and computational inefficiency. The multiscale stochastic particle (MSP) method based on the Fokker-Planck model has recently emerged as a tailored approach for multiscale non-equilibrium gas flows, specifically designed to maintain high accuracy and computational efficiency even in near-continuum regimes. In this work, the MSP method is extended to diatomic gas flows by incorporating internal energy modes. Specifically, a particle-based Langevin integration scheme is developed to model internal energy relaxation. Building on this formulation, a modified collision step is introduced within the MSP framework, employing the flux correction strategy. The resulting scheme is shown to exhibit second-order temporal accuracy in the near-continuum regime. The proposed method for diatomic gases is validated against a range of benchmark problems, including homogeneous relaxation, normal shock structures, and hypersonic flows over a cylinder and a 70-degree blunted cone. The MSP method provides reliable results with coarser grids and larger time steps, substantially reducing computational cost. These results demonstrate its potential as an efficient and accurate approach for multiscale hypersonic flow simulation.